A nearly Kähler manifold is an almost Hermitian manifold \((M,g,J)\)  such that \(\nabla J\)  is skew symmetric: \((\nabla _X J)X =0\)  for every vector field \(X\)  on \(M\) . Each of these can be decomposed as a Riemannian product of nearly Kähler manifolds which are either Kähler, 6-dimensional, homogeneous, or twistor spaces over quaternionic Kähler manifolds of positive scalar curvature [1]}. We will focus on the case of 6-dimensional nearly Kähler manifolds that are strict in the sense that they are not Kähler. These are characterized by being the links of metric cones with holonomy \(G_2\) , which makes them Einstein with positive scalar curvature [2]}.
